A classification of proper holomorphic mappings between generalized pseudoellipsoids of different dimensions
Atsushi Hayashimoto
TL;DR
This paper classifies proper holomorphic mappings between generalized pseudoellipsoids of different dimensions, revealing relations among domain parameters using CR bundle decomposition.
Contribution
It introduces a classification framework for proper holomorphic maps between pseudoellipsoids with different dimensions based on orthogonal CR bundle decomposition.
Findings
Derived relations among domain exponents
Established a variable-splitting technique for mappings
Provided a comprehensive classification of mappings
Abstract
We classify proper holomorphic mappings between generalized pseudoellipsoids of different dimensions. Those domains are parametrized by the exponents. The relations among them are also obtained. Main tool is the orthogonal decomposition of a CR bundle. Such a decomposition derives the `variable-splitting' of the mapping.
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Taxonomy
TopicsHolomorphic and Operator Theory · Geometry and complex manifolds · Algebraic and Geometric Analysis